Question: Solve for $x$ and $y$ using elimination. ${-5x-2y = -23}$ ${4x-5y = -41}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $4$ and the bottom equation by $5$ ${-20x-8y = -92}$ $20x-25y = -205$ Add the top and bottom equations together. $-33y = -297$ $\dfrac{-33y}{{-33}} = \dfrac{-297}{{-33}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {-5x-2y = -23}\thinspace$ to find $x$ ${-5x - 2}{(9)}{= -23}$ $-5x-18 = -23$ $-5x-18{+18} = -23{+18}$ $-5x = -5$ $\dfrac{-5x}{{-5}} = \dfrac{-5}{{-5}}$ ${x = 1}$ You can also plug ${y = 9}$ into $\thinspace {4x-5y = -41}\thinspace$ and get the same answer for $x$ : ${4x - 5}{(9)}{= -41}$ ${x = 1}$